PSEUDOLITE-BASED INVERTED POSITIONING AND ITS
Liwen Dai, Jinling Wang, Toshiaki Tsujii, Chris Rizos
School of Geomatic Engineering
University of New South Wales
Liwen Dai received a B.Sc. and M.Sc. in Geodesy in 1995 and 1998 respectively, from the
Wuhan Technical University of Surveying and Mapping (WTUSM), P.R. China, and then joined
the School of Geomatic Engineering, The University of New South Wales (UNSW), Sydney,
Australia, as a Visiting Fellow in November 1998. Since the start of 2000 he has been a full-time
Ph.D. student at UNSW where his current research interests are software and algorithm
development for rapid static and kinematic positioning (and attitude determination) using
integrated GPS, Glonass and pseudolite systems.
Jinling Wang holds a Ph.D. from the Curtin University, Australia. He is currently an Australian
Research Council Postdoctoral Fellow in the School of Geomatic Engineering, UNSW. Jinling
has authored over 100 refereed journal and conference publications, two widely-used commercial
software packages, and has received over 10 academic awards. He is Chairman of the Working
Group "Pseudolite applications in Engineering Geodesy", of the International Association of
Geodesy's (IAG) Special Commission 4, and a member of the Editorial Advisory Board of the
journal GPS Solutions.
Toshiaki Tsujii is a senior researcher of the Flight Systems Research Center, National Aerospace
Laboratory (NAL), Japan, where he has been investigating aspects of satellite navigation and
positioning for ten years. In Feb. 2000 he commenced a 2 year visit within the Satellite
Navigation and Positioning (SNAP) Group, at the School of Geomatic Engineering, UNSW, as a
JST postdoctoral research fellow. Toshiaki holds a Ph.D. in applied mathematics and physics
from Kyoto University. His current research interest is kinematic GNSS positioning of airborne
Chris Rizos, B.Surv. (UNSW) Ph.D. (UNSW), has been an academic staff member of the School
of Surveying (renamed the School of Geomatic Engineering in 1994) at UNSW, since 1987,
where he is now a Professor. Chris is leader of the SNAP group, a Fellow of the IAG and of the
Australian Institute of Navigation. He has published over 150 papers, as well as authored and co-
authored several books relating to GPS and positioning technologies.
In this paper, the pseudolite-based inverted positioning system, where a ‘constellation’ of GPS
receivers with precisely known 'orbit' tracks a mobile pseudolite, is described. The system
consists of an array of GPS receivers, the reference pseudolite (or reference GPS satellite) and the
mobile pseudolite. Two configurations of the inverted positioning system are discussed. The
implementation challenges for the pseudolite-based inverted positioning system, including
geometry optimization, multipath and receiver array location dependent errors have been
investigated. Several applications using the inverted positioning concept, including deformation
monitoring and navigation services based on pseudolite installed on stratospheric airships, are
A static experiment was carried out using six NovAtel GPS receivers and two IntegriNautics
IN200CXL pseudolite instruments, on the UNSW campus, on the 4th April 2001. The
experimental setup and operating procedures are described in detail. The carrier phase
measurements have been processed in an 'inverted' mode. The results indicate that the accuracy
of the inverted phase positioning is less 5mm. The static experiment has indicated that the two
configurations for the inverted positioning are feasible in practice.
Over the last decade or so, GPS positioning has played an increasing role in both surveying and
navigation, and has become an indispensable tool for precise relative positioning. However, in
some situations, such as in urban canyons, dam monitoring in valleys and in deep open-cut
mines, the number of visible satellites may not be sufficient to reliably determine precise
coordinates. Furthermore, it is impossible to use GPS for precise indoor positioning.
Pseudolites, which are ground-based transmitters of GPS-like signals (i.e. “pseudo-satellite”), can
significantly enhance the satellite geometry, and even replace the GPS satellite constellation in
some circumstances. The pseudolites typically transmit pseudo-range and carrier phase
measurements signals at one or both the GPS frequency bands (L1: 1575.42MHz; L2:
1227.6MHz). The use of pseudolites can be traced back to the early stages of GPS development
in the late 1970s, at the Army Yuma Proving Ground in Arizona (Harrington & Dolloff, 1976),
where the pseudolites were used to validate the GPS concept before launch of the first satellites.
In the mid 1980s, the RTCM committee SC-104 ('Recommended Standards for Differential
NAVSATR GPS Service') designated the Type 8 Message for the pseudolite almanac, containing
the location, code and health information of pseudolites (Kalafus et al., 1986). With the
development of the pseudolite techniques and GPS user equipment during the last decade,
pseudolites can now be used to enhance the availability, reliability, integrity and accuracy in
many applications, such as aircraft landing (Holden & Morley, 1997; Hein et al., 1997),
deformation monitoring applications (Dai et al., 2000; 2001a), Mars exploration (Lemaster &
Rock, 1999), precision approach applications, and others (Barltrop et al., 1996; Wang et al.,
PSEUDOLITE-BASED INVERTED POSITIONING CONCEPT
The concept of inverted pseudolite positioning was first introduced by Raquet et al. (1995). In
their experiment, a ground-based test was conducted to investigate the feasibility of using mobile
pseudolites for the precise positioning of military aircraft. O’Keefe et al. (1999) presented
experimental results and also discussed the pseudolite-based inverted GPS concept for local area
The pseudolite-based inverted positioning system consists of an array of GPS receivers, the
reference pseudolite (or GPS reference satellite) and the mobile pseudolite. There are two
configurations for an inverted positioning system (Figure 1), where the only difference is whether
the pseudolite is selected as the ‘reference’ (referred her as type I), or a GPS satellite (referred her
as type II). The reference satellite or pseudolite is needed to form double-differenced observables,
and to remove the receivers’ clock biases, as well as other code and phase biases. It should be
emphasized that both the type I&II configurations have the same Dilution of Precision (DOP)
factor because the DOP value is only a position function of the mobile pseudolite and receiver
Figure 1: Inverted positioning configurations
(Left: two pseudolites, and Right: a pseudolite and a GPS satellite).
There are different benefits and disadvantages for the two configurations respectively. In the type
I configuration, orbit error and atmospheric error related to the GPS reference satellite are
insignificant and can be ignored in the case of the short distances between the receivers.
However, in the type II configuration these errors related to the reference pseudolite may be
significant because of the short distances between reference pseudolite and receivers. Their
influences will be discussed in the next section. The type I configuration can overcome the
limitations of ‘satellite-based’ positioning indoors, for applications in tunnels or underground,
where GPS satellite signals cannot be tracked. Furthermore, all the hardware equipment and
software are configured on the ground, where the power, size and computational load constraints
can be easily resolved. However, in the type II configuration, one GPS satellite in view is
selected as the base reference and reduces the overall system cost. It is suitable for some
applications in urban canyons, dam monitoring in valleys and in deep open-cut mines, where the
number of visible satellites may not be sufficient to reliably determine precise coordinates.
Furthermore, in the type II configuration, GPS satellite time can be used to synchronize GPS
receivers within 1msec. However, system time synchronization may need to be addressed in the
Type I configuration.
IMPLEMENTATION ISSUES FOR AN INVERTED POSITIONING SYSTEM
In the pseudolite-based inverted positioning system, there are challenging implementation issues
that need to be addressed. These include: geometric optimization, multipath and receiver array
The receiver array geometry optimization refers to the need to find locations for the receivers and
the pseudolite transmitter that will minimise the Position Dilution of Precision (PDOP), Relative
Position Dilution of Precision, or others (in this paper, PDOP is used).
Poor geometry of receiver arrays were investigated by Pachter & Mckay (1998). If the receiver
array and pseudolite transmitter all lie approximately in the one plane, or the LOS vectors drawn
from the pseudolite transmitter to the receivers have similar angular orientations (i.e. the
pseudolite transmitter is very far away from the receiver array in the same direction), poor
geometry will result. Therefore the measurement errors in precise positioning will be greatly
amplified. A computer simulation showing the minimum PDOP values as a function of the
number of receivers is plotted in Figure 2 after the constraint that the receiver elevation angle
related to the mobile pseudolite cannot be less than 0 degree is applied. It can be seen that the
Figure 3: Optimum four-receiver array to minimise
PDOP value. R1-R4 indicates the location of the 4
Figure 2: Minimum PDOP values. receivers and the mobile pseudolites are indicated PL.
Figure 5: Minimum PDOP as a
Figure 4: PDOP as a function of 'key
function of cut-off angle for four
receiver' elevation and azimuth.
PDOP values will reduce when the number of receivers increases. For a four-receiver array the
minimum PDOP values still can reach 1.63. The simulation also shows that if the receivers are
equally spaced in the azimuthal plane, and at a zero elevation angle related to the mobile
receivers, and one receiver (called the 'key receiver') is at the zenith, the minimum PDOP values
can be obtained. Figure 3 shows the optimization configuration in the case of a four-receiver
array. It has been found that the 'key receiver' is very important for decreasing the PDOP values.
Figure 4 shows the PDOP values related to the 'key receiver' azimuth and elevation angles. It can
be seen that when the elevation angle of the 'key receiver' decreases, PDOP value will
significantly increase. The optimization of PDOP values is difficult to obtain in practice. Figure 5
shows the minimum PDOP values as a function of the elevation cut-off angle for a four-receiver
array configuration. It should be emphasised that very good geometry can still be obtained
(PDOP value less than 3) even though the cut-off angle is up to 30 degrees. This fact ensures
flexibility when considering receiver array optimization.
Receiver Array Location Error
The receiver array with known coordinates is essentially considered like a GPS satellite
constellation on the ground in the inverted positioning system. Due to the short distances between
the pseudolite and the receivers, the influence of receiver location dependent errors (which are
similar to pseudolite location bias in the case of GPS positioning augmented by pseudolites) must
be considered in a different way to that of GPS satellite orbit bias. Their effects have been
analysed in detail (Dai et al, 2001a; Wang et al, 2001). Due to the ‘satellites’ (i.e. static receivers)
being stationary (unlike the moving GPS satellites) the receiver-location bias will be a constant.
If the reference and mobile pseudolite are both stationary, orbit error will contribute an invariant
bias to the differenced observables. In the worst case, the influence of the receiver-location bias
on the differenced range becomes doubled. The receiver-location errors can bias significantly the
precise carrier phase observation even though they are only of the order of a few centimetres in
magnitude. Good selection of receiver location can mitigate the effect of this bias. It also should
be emphasised that for kinematic applications the receiver location should be precisely
determined beforehand, using GPS surveying, 'total station' or other traditional surveying
The multipath from pseudolites is not only due to reflected signals from the surface, but also
from the pseudolite transmitter itself (Ford et al., 1996). Bartone (1999) has shown that the
standing-wave multipath in an airport pseudolite ground-to-ground link can essentially be
eliminated by the use of a Multipath-Limiting-Antenna for both the pseudolite transmission and
reception antennas. If the pseudolite and receiver are both stationary, the multipath bias will be a
constant. Hence, the influence of multipath from pseudolites cannot be mitigated and reduced to
the same extent over time as in the case of GPS. Therefore the multipath will significantly
increase the noise level of the measurement in a dynamic environment, because it is very hard to
avoid, even though careful precautions may have been taken. However, because of the constant
characteristics of the multipath from a pseudolite transmitter in a static environment, it is
relatively easy to calibrate it in advance. The constant (or very near invariant) bias can be
predicted and removed during data processing, and pseudolite signals can, in principle, make a
contribution to improving the performance for some static applications. Pseudolite multipath is a
challenging issue that needs to be solved for kinematic applications. Good hardware design,
including receivers, receiver antennas and pseudolite transmitter antennas, as well as software-
based multipath mitigation techniques will be needed.
INVERTED POSITIONING APPLICATIONS
Based on the pseudolite inverted positioning concept, two applications – deformation monitoring
and navigation services based on pseudolite installed on stratospheric airships – have been
investigated at the UNSW.
As is well known, GPS techniques cannot be used when the signals are completely blocked by
obstacles – natural and man-made. However, monitoring of man-made structures may be needed
in areas such as canyons, or underground and in tunnels. In these situations, GPS-only
deformation monitoring is impossible. The potential deformation monitoring applications using
the pseudolite-based inverted positioning concept has been investigated by the authors (Dai et al.,
2001b). This can extend the concept of ‘satellite-based’ deformation monitoring indoors, for
applications in tunnels or underground, where GPS satellite signals cannot be tracked.
Applications with implementation constraints such as solution reliability and availability, and
severe design constraints such as space and weight could be addressed by the pseudolite-based
inverted positioning technique. In this system, more flexibility is obtained and cost is reduced
because all the hardware equipment and software are configured on the ground, where the power,
size and computational load constraints can be easily resolved. Furthermore, the whole system
may be able to operate in the presence of jamming at GPS frequencies. In practice, constant
systemic biases from multipath, and the receiver array location-dependent bias can be calibrated
Navigation Services Based on Pseudolite Installed on Stratospheric Airships
Feasibility studies and R&D projects on high altitude platform systems are being conducted in a
number of countries. Japan has been investigating the use of an airship system that will function
as a stratospheric platform (altitude of about 20km) for applications such as environmental
monitoring, communications and broadcasting. Remote sensing from such an airship would be
very effective because it floats above the same ground area, permitting continuous monitoring of
the surface. However, the precise positioning of the airship is one of the most important technical
challenges for such a project. If the pseudolite transmitter is installed underneath an airship, its
position can be precisely determined by the receiver array on the ground using the inverted
positioning method (Tsujii et al., 2001). In addition, the pseudolites could be considered as
additional GPS satellites, which would improve the accuracy, availability, and integrity of GPS-
based positioning systems.
TEST RESULTS AND ANALYSIS
A static test was carried out to investigate the feasibility of the pseudolite-based inverted
The experiment was conducted using six NovAtel receivers (four MillenniumTM and two
BeelineTM) and two IntegriNautics IN200CXL pseudolite instruments on the UNSW campus on
the 4th April 2001. The two pseudolites were configured as PRN codes 12 and 16. The six
receivers were sited on the roof of the electrical engineering building (Figure 6). The pseudolites
transmitted only GPS L1 signals. In order to avoid signal interference, the RTCM recommended
pulsing signals at 1/11 cycle was used, and 32 dB attenuation was applied to the signal power.
Figure 6: Location of instruments for inverted positioning experiment, 4th April 2001. A1-A6
indicates the location of the 6 receivers and the two pseudolites are indicated as Ref PL and
In the case of the NovAtel receivers, channels can be easily assigned to the specified PRNs to
track pseudolite signals. The remaining channels were used to track GPS satellite signals. About
40 minutes of GPS and pseudolite measurements were collected with one-second sampling rate.
The coordinates of the six receivers and two pseudolite sites were precisely determined
beforehand using the GPS receivers. The number of the receivers tracking both pseudolites was 5
Figure 7 shows the HDOP (Horizontal Dilution of Precision) and VDOP (Vertical Dilution of
Precision) values of the mobile pseudolite PL16 during the experiment. Although 5-6 receivers
tracked both pseudolite signals, the different combinations of receivers results in different HDOP
and VDOP values. It can be seen from the Figure 7 that very good geometry (HDOP and VDOP
both less than 2) was obtained because of the optimized receiver locations through careful
selection of antenna locations.
Figure 7: The HDOP (Left) and VDOP (Right) values.
Carrier phase ambiguity resolution could not be attempted in the normal manner because the
receivers and pseudolites are stationary. The carrier phase processing was conducted by rounding
off the double-differenced ambiguity to the nearest integer using the known initial position of the
mobile pseudolite. During data processing it was found that significant constant biases existed in
the pseudolite carrier phase measurements. The constant biases may come from the invariant
multipath, because of high multipath environment in the roof. The carrier phase multipath for the
one-way signal does not exceed about one-quarter of the wavelength (5-6cm for L1 or L2).
However, the double-differenced measurements, involving four one-way signals, could be
seriously contaminated by multipath. It is therefore necessary to calibrate the constant biases in
static environment before data processing. In this experiment, each receiver not only tracks the
two pseudolite signals but also the GPS signals. Therefore GPS measurements can be used to
calibrate the residual biases in the pseudolite measurements. Figure 8 shows the values of the
double-differenced L1 residual biases between receivers and two pseudolites, or one pseudolite
and one GPS satellite. The constant biases for receivers 1, 2, 3, 4, 5 are -0.0742, 0.0918, 0.2048,
0.0446 and 0.1663 cycles in the type II configuration, and 0.3374, -0.3477, 0.0747, -0.0688, -
0.1288 cycles in the type I configuration (receiver 6 was selected as the reference ‘satellite’). It
should be pointed out that the RMS of these bias values are less than 1cm (0.05 cycle).
Figure 8: Double-differenced L1 residuals (Left: type II, and Right: type I).
The data was processed in single-epoch mode using both configurations (type II&I). The highest
satellite (PRN7) was chosen as the reference ‘receiver’. The positioning results are plotted in
Figure 9. The RMS of the North, East and Height components are 2.6mm 5.0mm and 4.9mm in
the type II configuration, and 2.9mm, 4.7cm and 4.8mm in the type I configuration respectively.
Because the constant biases in the pseudolite carrier phase measurements are calibrated
beforehand, the positioning solutions are not biased. The conclusion can be made that high
accuracy positioning results can be achieved using both the type I and II configurations.
Figure 9: The East(upper plot), North (middle plot) and Height (lower plot) results for
inverted carrier phase positioning (Left: type II, and Right: type I).
In this paper, two configurations for a pseudolite-based inverted positioning system have been
described. Some implementation issues, such as systemic biases, receivers' geometry
optimization and pseudolite signal interference, have been investigated.
The static experiment was carried out using six NovAtel GPS receivers and two IntegriNautics
IN200CXL pseudolites, and the experimental results indicate that the accuracy of the height
component can indeed be significantly improved (the RMS of vertical was reduced by a factor 4),
to approximately the same level as the horizontal components. Pseudolite multipath is a
challenging issue that needs to be solved for kinematic applications. Good hardware design,
including receivers, receiver antennas and pseudolite transmitter antennas, as well as software-
based multipath mitigation techniques will be needed.
The first author is supported by an International Postgraduate Research Scholarship (IPRS). The
authors also would like to thank Graham Boyd, Normandy Exploration, for kindly providing four
NovAtel receivers, and their colleagues Joel Barnes and Craig Roberts for their assistance in
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